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Condens. Matter 2019, 4, 86 5 of 15 Figure 2. The XRD patterns of the LiFePO4 sample at room temperature. Experimental points are represented by red circles, whereas the green curve shows the fitted spectrum. Main peak indices are also given along with the peak positions (bottom part of the figure). Figure 3 displays the temperature dependences of the zero field cooled (ZFC) and the field cooled (FC) magnetizations, σ(Z)FC, under an applied magnetic field of 1 T. The results show a typical antiferromagnetic transition at TN = 52 K and a decrease in the magnetization with the decreasing temperature below TN. For temperatures T > TN, the molar susceptibility, χm, see Figure 3, was fitted to the Curie-Weiss law χm = C/(T + Θ); C and Θ are constants related to the measured system (LiFePO4) and observed magnetic phase transition. The Curie constant C = μ0NAμ2eff/3kB , with μ0 being the vacuum permeability, NA the Avogadro constant, kB the Boltzmann constant, and μeff the effective magnetic moment. The fitted values are Θ = −91(2) K and C = 4.6(1) × 10−5 m3K/mol. From the Curie constant C, the value μeff = 5.5(1) Bohr magnetons (μB) is obtained, in good agreement with Θ = −92(1) K and μeff = 5.58(1) μB reported in Reference [36] (see also Reference [17]). The effective magnetic moment is slightly higher than μeff = 4.90 μB for Fe2+ in the high-spin state (S = 2) with the orbital angular momentum quenched (L ≈ 0) by the crystal field. The theoretical value of the high spin state of the free Fe2+ ion (S = 2, L = 2) is μeff = 6.71 μB. A higher value of μeff observed here thus indicates that the orbital angular momentum was not fully quenched by the crystal field. This observation is consistent with a non-zero orbital Fe2+ magnetic moment deduced from ab initio calculations discussed below. We mention an increase of the magnetization below temperature ∼ 17 K (Figure 3). Such an increase of the magnetization in LiFePO4 has also been reported in References [14,17,36]. Rhee et al. [17] related this effect to the influence of the spin-orbit coupling when it becomes comparable with the thermal energy at about 20 K, which results in an ‘unquenching’ of the orbital magnetic moments of Fe2+ ions, thus increasing their total magnetic moment.PDF Image | Mossbauer Spectroscopy of Triphylite (LiFePO4) at Low Temperatures
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